Anticipating nitpickers, I’ll np my own post:
I’m well aware that Spain did not exist as a political entity when Catallus was writing, and that Sir Richard spoke and wrote in Modern English. 
I dunno, but your question reminded me of a similar oral hygiene tip:
My Dad used to say that chicken shit is good for chapped lips.
…It won’t heal your lips, but it’ll damn sure make you stop licking them.
Thanks samclem here is the Wikepedia article.
It doesn’t say anything not said above except it posits that the Amonia in Urine might actually have a whitening effect. Now I know of amonia being used to bleach things, but any Chemist out there want to give there views? Also wouldn’t other contents of urine cancell the effect, after all urine stains are usually pale yellow rather than bleached white. Would urine have a whitening effect or just die teeth a lighter yellow than their uncleaned colour?
Thanks Bippy the Beardless.
I’ve done some more research on the matter and I suspect that the urea may have more of a whitening effect than the ammonia. Many of the commercial whitening products contain Urea Peroxide a.k.a. Carbamide Peroxide:
http://www.toothwhite-info.com/toothwhite-colgate.htm
“Ingredients: Alcohol, Water, Urea Peroxide (Carbamide Peroxide), PEG 2M, Glycerin, Carbopol, Sodium, Phosphate and Phosphoric Acid”
This doesn’t follow.
Urea and urea peroxide are not the same thing. Urea peroxide is a compound of urea and hydrogen peroxide, which breaks down in alkaline saliva, creating the bleaching effect. It’s the peroxide that’s whitening.
Ordinarily, urine does not contain peroxides, unless something is seriously wrong. Simple urea will not whiten your teeth.
Slightly off topic (or maybe not)…but in the Baroque Cycle series of books by Neal Stephenson, some of the main characters make large quantities of phosphorus from boiling urine.
So does urine brighten the teeth by giving them a phosphorescent glow along with etching off all the crud, or do you just get the phosphorescent glow?
And again with the off topicness - in the Clan of the Cave Bear book series (I know, I know), there are depictions of stale urine being used to bleach tanned hides until they become pretty white (according to the depictions therein). The staleness is key - apparently something to do with the ammonia.
And I believe some of our more handy Dopers have testified to using urine during their various dyeing processes - helps to set the colors.
I’m pretty sure I’m not going to use it on my teeth, however.
Here is a link to use of urine in the Fuller’s trade. http://www.unc.edu/courses/rometech/public/content/survival/DeRamus_Durham_Laxton/margaretfin.html
This thread brings to mind a quote from one of my favorite movies:
“Sewer rat may taste like pumpkin pie, but I’d never know 'cause I wouldn’t eat the filthy motherfucker.”
-rainy
Fresh urine has little ammonia, which is highly toxic. Instead it contains less-toxic urea, which can be broken down into ammonia by bacterial action. So if it’s ammonia you’re after, you have to let the urine age a bit.
Highly recommended: BBC Radio 4’s documentary “Taking the Piss Out of London,” which documents the economic and industrial importance
of urine into the 20th century.
After hearing about fullers and what they worked with, I always grin while drinking Fuller’s Ale. 
Apart from fullery, urine was crucial as a precursor for textile dyes. Urine was collected in London and brought by boat to the shale quarries at Yorkshire. Shale was burned to ash and stale urine was poured over it, which produced valuable alum, which was important for dyes. (Supposedly, the first public urinals in Hull were established to prevent a valuable resource from being lost against walls – wee produced at home was set out in buckets for collection.)
Anyway, part of the story is that this trade produced a whole class of nouveau riche who tended to be a little evasive about the source of their wealth. They’d say things like “I transport wine.” Canny people would then conclude, “Oh, he’s taking the piss,” which is how that expression supposedly became a way of saying “That’s not quite true, and you can’t fool me.”
I suspect that that origin might itself be a piss-take, though – it’s just a little too pat.
Was urine the best source of amonia in the pre-industrial world?
Thanks, samclem – I was fairly certain that was a dubious etymology.